Question

Simplify completely quantity x squared plus 4 x minus 45 all over x squared plus 10 x plus 9 and find the restrictions on the variable.
A) quantity x minus 5 over quantity x plus 1, x ≠ −1, x ≠ −9
B) quantity x minus 5 over quantity x plus 1, x ≠ −1, x ≠ 5
C) quantity x plus 5 over quantity x plus 1, x ≠ −1, x ≠ −9
D) quantity x plus 5 over x plus 1, x ≠ −1, x ≠ 5

Answer 1

Answer:

A) Quantity x minus 5 over quantity x plus 1, where x≠-1 and x≠-9

Step-by-step explanation:

$\frac{x^2 + 4x - 45}{x^2 + 10x + 9}$

Simplifying the numerator first:

x² + 4x - 45 using the quadratic formula you get;

(x - 5)(x + 9)

Then simplifying the denominator x² + 10x + 9 using a quadratic formula you get;

(x + 1)(x + 9)

Dividing the numerator and denominator now gives;

$\frac{(x - 5)(x + 9)}{(x + 1)(x + 9)}$

Cancelling (x + 9) throughout leaves you with;

$\frac{x - 5}{x + 1}$

The only restrictions here is if x = 1 and 9 which will give an undefined answer.

Answer 2

Answer:

Step-by-step explanation:

) Quantity x minus 5 over quantity x plus 1, where x≠-1 and x≠-9